Algebraic theory of Stark-Zeeman dynamic effect in hydrogen-like atom

The problems of calculating time evolution operator within the given n-shell (here n is main quantum number) for the hydrogen atom located in non-stationary electric and magnetic fields is under investigation. Making use of the Fock SO(4) group reduces this problem to the set of problems with linear realization of the dynamic symmetry group for which the evolution operator is the operator of corresponding groups representation. The types of evolution operator parametrization in the form of exponents product (the Wei-Norman method) any by means of D-functions connected with Euler angles and Cayley-Klein parameters are discussed. It is shown that the problem of evolution operator calculation can be reduced to investigation of a pair of two-level systems. 35 refs